Interspecific Pollen Transfer and Competition between Co-Occurring Plant Species

Transcription

1 Oecologia (Berl.) 36, (1978) Oecologia 9 by Springer-Verlag 1978 Interspecific Pollen Transfer and Competition between Co-Occurring Plant Species Nickolas M. Waser* Department of Ecology and Evolutionary Biology, University of Arizona, Tucson, AZ 85721, USA Summary. Computer simulations of a pollinator foraging in a mixture of two species were', used to explore how plant reproduction can be influenced by interspecific pollination movements. Interspecific pollen transfer led to strong competitive effects when availabilities of pollen, receptive stigma surfaces, or pollinator movements were limited relative to the total number of fertilizations possible in the mixed population. Results from simulations suggest that competition for pollination through interspecific pollen transfer can result in rapid exclusion of one of two species, and that such competition represents a selective force promoting stable divergence of potential competitors in habitat affinity, flowering time, or other characteristics related to pollinator sharing. Introduction At the end of the last century, the botanist Charles Robertson proposed that competition for pollination among flowering plants could be a major force promoting evolutionary divergence in characteristics related to pollinator sharing. He reasoned (1895, p. 100) that in order to avoid competition, co-occurring species should alter their habitat or pollinator affinities or "'... separate their times of blooming so that they will not have to compete with a great many similar flowers for the attention of the same kinds of insects." Recently, the impact of competition for pollination on the temporal, spatial, and morphological structure of plant communities has received general attention (e.g., Grant, 1950; Macior, 1970; Mosquin, 1971 ; Heinrich, 1975; Reader, 1975; Stiles, 1975; Feinsinger, 1976; Lack, 1976; Waser, 1977, 1978), and discussion of mechanisms by which pollinator sharing may lead to competition has been initiated by Levin and Anderson (1970) and Straw (1972). * Present address." Department of Biology, University of Utah, Salt Lake City, UT 84112, USA /78/0036/0223/$02.80

2 224 N.M. Waser When two or more co-occuring species overlap in their flowering times and attract at least one pollinator in common, a reproductive disadvantage may accrue to individuals of each species which flower in the presence of the other species relative to those which flower alone. To be consistent with the usage of competition theory (e.g., MacArthur, 1972, p. 34ff. ; Emlen, 1973, p. 306ff.), I define such a reproductive loss as competition whatever the mechanisms that produce it. In fact, two types of mechanism have been proposed to lead to a reproductive loss through pollinator sharing. According to the most commonly discussed mechanism, one plant species can reduce rates of visitation and pollination to others by being more attractive to pollinators (e.g., Clements and Long, 1923; Free, 1968; Mosquin, 1971; Straw, 1972; Reader, 1975; Lack, 1976). According to the second type of mechanism, interspecific movements of pollinators foraging without preference in multispecies mixtures can by themselves lead to reproductive effects (Lewis, 1961; Levin and Anderson, 1970; Waser, 1978). There are several different ways in which interspecific pollinator movements might lead to reproductive losses. Since these have not been discussed clearly in the past, I describe them here in some detail. Consider as the simplest system two plant species which flower simultaneously and are visited without preference by pollinators. Because a pollinator chooses successive plants with no regard for their species identity, some proportion of the plant-to-plant movements it makes will be interspecific. If such movements transfer pollen they can cause a reproductive loss in several ways. First, interspecific pollen transfer will lead to a loss of pollen for individuals of both species since some pollen will be deposited on foreign stigmas or other floral parts. Second, interspecific pollen transfer will lead to a loss of receptive stigma surface area for both species whenever their anthers deposit pollen on overlapping parts of the pollinator's body, since stigmas will then pick up some foreign pollen. Finally, interspecific pollen transfer will lead to a loss of effective pollinator visits themselves. The magnitude of this last effect should depend in part on the degree to which pollen picked up at any flower is carried over past the first recipient flower; with no carryover all interspecific movements will be lost to the reproduction of both plant species. If reproduction of either species is potentially limited by the availabilities of pollen, stigma surface areas, or pollinator visits, the loss of these three commodities as a result of interspecific pollen transfer will lead to competition. As I will outline in the discussion section, available evidence suggests that there is no surplus of pollen or stigma surfaces in many systems. Although it has received relatively little attention in the past, competition for pollination through interspecific pollen transfer is likely to be of general importance because it can occur even in the absence of pollinator preference or of obvious limitation in pollinator numbers. Furthermore, this type of competition may have unique evolutionary consequences because its effects are frequency dependent, lead to reciprocal reproductive losses to each of two cooccurring species, and should therefore promote stable divergence in floral characteristics affecting pollinator sharing (cf. Levin and Anderson, 1970; Waser, 1977). In contrast, competition through pollinator preference should often lead to exclusion of all but the most attractive plant species, since this species will cause reproductive losses to others without suffering reciprocal losses itself.

3 Interspecific Pollen Transfer and Competition 225 In this paper I use computer models to explore competition through interspe- cific pollen transfer. The models simulate pollination of two plant species by a shared pollinator foraging without preference, and they allow me to manipulate directly the availabilities of pollen, stigma surfaces, or pollinator visits to the two species and to see how this influences their competitive interaction. The results from simulations agree with those from corresponding deterministic mo- dels (Levin and Anderson, 1970; Waser, 1977) in suggesting that interspecific pollen transfer in a two-species mixture can lead to competitive exclusion of one species. In addition, they suggest situations of evolutionary differentiation of competitors which will allow their stable coexistence in nature. Simulation Programs In designing simulations I attempted to retain simplicity without straying from biological realism. The assumptions built into the models about the mechanics of pollination are generally in good agreement with available empirical data, as I will explain in detail in the discussion section. I will gladly supply copies of computer programs on request. The basic program simulates the progress of a pollinator foraging in a population containing two plant species, A and B. The population is represented by a 10 by 10 array, and each array location contains at most one plant. Plants of each species produce only one flower and live for one generation. A pollination bout begins at a random array location and progresses in unit movements between neighboring flowers until a movement causes the pollinator to leave the array. At this point a new bout is initiated. This process continues within each computer generation until a set total number of pollinator movements has accumulated. Diagonal movements between array locations are not allowed and probabilities of moving in each of the four possible directions upon leaving each flower are equal. Flowers of both species are assigned an equal initial number of pollen grains in their anthers. Each pollinator visit depletes this supply by a constant amount until it is exhausted. The pollinator carries no pollen at the beginning of a bout, but picks up a set load from the first flower visited and from each successive flower whose pollen supply is not exhausted. At each flower visited the pollinator deposits a constant number of pollen grains chosen at random and without replacement from the supply on its body. Pollen is considered to accumulate on a stigma of limited capacity, and each conspecific grain deposited gives rise to a viable seed of that species. The plants constituting the first generation in the array are chosen at random and without replacement from a pool of 1000 seeds of each species so that the initial frequencies of species A and B are close to 0.5. The plants constituting each subsequent generation are chosen in the same way from the finite seed pool resulting from pollination in the immediately preceding generation. In order to explore effects of gene flow between separate plant populations, I wrote a second main program which extends the basic program by simulating pollination in a 3 by 3 arrangement of 10 by 10 arrays each containing species A and B. Different amounts of pollen and seed transfer are allowed to occur between these 9 arrays. Once again, the plants constituting the first generation in each array are chosen from initial pools of 1000 seeds of each species. I verified the performance of all programs with the aid of a subroutine which lists the sequence of flowers visited in a generation, their locations in the array or arrays, and the pollen contents of their stigmas. From this information, the proportions of A and B seeds produced in any generation were calculated by hand and compared with those produced by representative simulations. Results This section of the paper is divided into five parts. The first three parts describe simulations with a single 10 by 10 array and explore effects of varying availabilities of pollinator visits, pollen, and stigma surfaces, as well as effects of relaxing

4 226 N.M. Waser Table 1. Values of parameters used in simulations. For descriptions of parameters see "Simulation Programs" section and appropriate parts of "Results" section. Multiple values separated by slashes indicate parameters variedin a setof simulations. Values of additional parameters of pollen and seed flow used in part (5) of "Results" section are not shown Results Move- Initial Pollen Pollen Capa- Pollen Refugial Num- Edaphic section, ments pollen grains grains city compe- areas ber barriers part: per supply picked depos- of tition of seed genera- up ited stig- on choices tion mas stigmas (1) 25/100/ no (2) 25/100/ yes (3) 100 3/10/ no (4) yes 10/20/40% 1/2 absolute yes 10/20/40% 2/4 partial (5) yes the stipulation that array locations are assigned to individuals of either species at random. The last two parts describe simulations with nine separate arrays and explore effects of seed and pollen exchange between populations. Table 1 summarizes values of various parameters of the model used for the simulations described in each part of the "Results" section. (I) Pollinator Movements Limiting Pollinator movements will be limiting to the reproductive output of both species in a mixture if the number of movements allowed in each computer generation multiplied by the number of pollen grains deposited per movement is small relative to the total number of fertilization events possible. Figure 1 A shows the number of generations to fixation for one or the other species from sets of 20 replicate simulations with 25, 100, or 400 movements per generation and three pollen grains deposited per movement. In all cases, there were 500 possible fertilizations per generation, because for each of 100 flowers a stigma surface was specified which could accept five pollen grains. Foreign grains were not counted toward this total of five. Initial pollen supplies in anthers were not limiting (100 grains per flower), nor were pollen loads picked up during each pollinator visit to a flower (10 grains). Under these conditions the shortest mean duration of coexistence of species A and B occurred with 25 movements per generation. Coexistence was extended by about three generations with 100 movements per generation and by a further three generations with 400 movements per generation. Without the constraints of limited pollen or stigma surfaces, further increases in the number of movements per generation should eventually lead to total fertilization of both species. At this point, the composition of the mixture would depend on sampling error in the choice of the 100 seeds which constitute each generation.

5 Interspecific Pollen Transfer and Competition 227 x E 20 "1 A~ WITHOUT POLLEN COMPETITION V-- // uj 0 f t I Z 0 ~5 C, ~,O- ~ B~ I~//t~ WITH POLLEN COMPETITION ; ~z ~, 0 i 15- z A_; ONE SEED CHOICE O IO- X 0 5- I-- Z 0 0 I-- Z I~1 15- t..9 W I0-,.=, C u-e g~ z o,,,,,, == o ~,; I;o O0 400 z 1 MOVEMENTS PER GENERATION 2 INITIAL POLLEN SUPPLY 3 I [ I B_z" TWO SEED CHOICES I I I IO% 20% 40% REFUGIAL AREAS Fig. 1A and B. The effect of varying the number of pollinator movements per generation on the number of generations to fixation for one or the other species, A without and B with interspecifie pollen competition on stigma surfaces. Each bar graph indicates the mean (horizontal line), +two S.E. (solid bar), and range (vertical line), from 20 replicate simulations Fig. 2. The effect of varying the initial pollen supply in anthers on the number of generations to fixation. Simulations specified 100 movements per generation and no potlen competition on stigmas. Bar graphs are as in Figure I Fig. 3A and B. The effect of size of refugia on the number of generations to fixation, A with one and B with two seed choices per refugiai location. Simulations specified 100 movements per generation, pollen competition on stigmas, and no chance of establishment of seeds in the improper refugium. Bar graphs are as in Figure 1 (2) Stigma Surfaces Limiting To see how the limitation of stigma surfaces influences the duration of coexistence of species A and B, I ran a set of simulations identical to those just described except that all pollen grains failing on a stigma were counted toward the total of five grains which saturate its surface. This allows foreign pollen reaching the stigma to block fertilization by conspecific grains deposited in a subsequent pollinator visit. Figure 1B shows the effect of this additional competitive mechanism. With 25 movements per generation, the mean duration of coexistence was equivalent to that without pollen competition on the stigma surface (Fig. 1 A). However, coexistence was extended by only about two generations with 100 movements per generation, and by only an additional fraction of a generation with 400 movements per generation. This suggests that an asymptote was being approached at which the effect of pollen competition on stigma surfaces dominated in determining the rate of fixation of one species, and at which additional increments in the number of pollinator movements per generation would not ensure longer periods of coexistence. (3) Amounts of Pollen Limiting If the initial supply of pollen in the anthers of flowers is small relative to the total number of possible fertilization events in the population, the loss

6 228 N.M. Waser of pollen as a result of interspecific pollen transfer may limit reproduction even in the absence of competition for limited pollinator movements or stigma surfaces. I investigated this prediction in simulations with 100 movements per generation and pollen loads of 10 grains picked up during each visit to a flower, and without pollen competition on stigmas. Figure 2 shows the results for initial pollen supplies in anthers of 3, 10 and 100 grains. An appreciable decrease in the duration of coexistence appeared only below 10 grains per flower, suggesting that amounts of pollen are not limiting above this value, given 500 possible fertilization events in the population. (4) Effects of Refugia In simulations discussed to this point I assigned all array locations to individuals of species A or B at the onset of any computer generation by choosing at random from the seed pool produced in the immediately preceding generation. Such a procedure can be interpreted to model a situation in which the two species grow equally well at all array locations, and so effectively compete for space as well as for pollination. Reduced spatial competition might delay or prevent the competitive exclusion that invariably occurred in previous simulations. I explored this possibility by introducing refugia for each species in which the competitor has either a reduced or no chance at all of establishment. Refugia of different sizes were established with a subroutine for assigning array locations which reserves a certain number of columns on either side of the array for each species. To determine occupants of array locations in these refugia, a seed is chosen at random from the seed pool as before. If it is of the proper species for that refugium, it is considered to germinate, but if not another seed is chosen. This process is repeated for a set number of seed choices. If none of the seeds chosen is of the proper species the subroutine either specifies that no plant colonize that array location or that one of the improper species do so. These alternative stipulations can be taken in the first case to imply an absolute edaphic barrier to establishment of plants in the improper refugium, and in the second case a strong barrier to establishment in the presence of a seedling of the proper species. The simulations did not count pollinator movements to empty refugial locations toward the total number in each generation. Pollen competition on stigma surfaces was allowed in all cases. The results from these simulations appear in Figures 3 and 4. Figure 3A shows the number of generations to fixation for one or the other species from sets of 20 replicate simulations with 100 pollinator movements per generation and refugial areas for each species of one to four array columns, or 10% to 40% of all array locations. In all cases, there was a single seed chosen to colonize each refugial location and an absolute barrier to establishment of seeds of the improper species. With refugial areas for each species of 10%, the mean duration of coexistence did not differ appreciably from that for simulations with identical parameters but without refugia (see Table 1 and Fig. 1 B). Coexistence was extended slightly with refugial areas for each species of 20% and 40%. Figure 3B shows the results of choosing a maximum of two seeds

7 Interspecific Pollen Transfer and Competition 229 O I J I 15-! a~ "~ = 4.40 Z o A. TWO SEED CHOICES 5 S =2.72 <~ ~O- X >- 0 ;,"," - E o 5- IO" O. X = LU S = 3.24 o 0 II: I I i LI. 5 v,, ili "' IS- Z I0-,,=, U-' POLLEN FLOW =0"9 ~=4"70S = 2,00 1! 5 z 0 lo 5 m A..: = 4. IO S = 2.02 POLLEN FLOW : O. I SEED FLOW= OJ II I-. r f i f i f [ POLLEN FLOW = O, I SEED FLOW = 0.2,- -,, l, POLLEN FLOW = 0.9 SEED FLOW = ~ POLLEN FLOW = o,r ~= 4,90 ~:,.,~,-,,,--,-,,,-', ~ POLLEN FLOW = 0,9 I. ' ~ 'IIIr.... ' SEED FLOW = 0'2..I,,...! I I I i ~ I E i i I i 0 I J I I I ~ I I 10% 20% 40% 0 I I REFUGIAL AREAS 5 POPULATIONS FIXED FOR (~ POPULATIONS FIXED OR NEAR SPECIES A FIXATION FOR SPECIES A Fig. 4A and B. The effect of size of refugia on the number of generations to fixation, A with two and B with four seed choices per refugial location. Simulations specified 100 movements per generation, pollen competition on stigmas, and a conditional chance of establishment of seeds in the improper refugium. Bar graphs are as in Figure 1 Fig. 5A and B. The effect of pollen flow on coexistence over nine separate arrays. Simulations specified probabilities of pollinator flight between adjacent arrays ("pollen flow") of A 0.1 and B 0.9. Histograms represent fi:equency distributions of the number of arrays out of nine which reached fixation for species A, fiom sets of 10 replicate simulations. In each case there were 900 pollinator movements per generation Fig. 6A-D. The effect of combined seed and pollen flow on coexistence. Simulations specified different probabilities of choosing seeds from a common pool ("seed flow") and of pollinator flight between adjacent arrays ("pollen flow"). Histograms represent frequency distributions of the number of arrays out of nine which reached or approached within 20% of fixation for species A after 15 generations, from sets of 10 replicate simulations. In each case there were 900 pollinator movements per generation as potential colonists for each refugial location, again with an absolute barrier to the establishment of seeds of the improper species. Under these conditions the mean duration of coexistence increased by about two generations as refugial areas were increased from 10% to 40%. Figure 4A shows the results of again choosing a maximum of two seeds for each refugial location, but now allowing establishment of a seed of the improper species if no seed of the proper species is chosen. An increase in refugial areas from 10% to 40% caused only a very slight increase in the mean duration of coexistence of the two species. Figure 4 B shows the results of choosing a maximum of four seeds again allowing establishment of a seed of the improper species. In this case coexistence was extended by about one generation with refugia of all sizes relative to the case with two seed choices (see Fig. 4A). In all simulations the period of coexistence increased as refugia became larger, as the number of seed choices per location

8 230 N.M. Waser was increased, and as the barrier to the establishment of seeds in the improper refugium was strengthened. Presumably, a complete barrier to establishment could allow coexistence of species A and B by removing competition for space, as long as the numbers of seeds produced per flower and of seed choices per refugial location are large enough to compensate for wastage of seeds falling in the improper refugium and wastage of pollinator movements, pollen, and stigma surfaces. (5) Pollen and Seed Flow between Separate Arrays To this point I have discussed the effects of pollen flow within a single array. I now introduce the possibility of pollen exchange between arrays, using simulations with a 3 by 3 set of arrays containing mixtures of species A and B. In the course of each computer generation at least one pollination bout is initiated in each of the nine separate arrays. If the pollinator moves beyond the edge of any array during a bout and has not left the overall set of arrays, there is a specified probability that it will fly to the nearest flower in the adjacent array as opposed to beginning a new bout at a random location in the array it has just left. Such a flight represents an event of pollen flow between arrays. I first explore the effect of pollen flow between arrays on the overall outcome of competition for pollination in cases where seeds are dispersed only within and never between arrays. Figure 5A and B shows frequency distributions of the number of arrays out of nine which reached fixation for species A, from sets of 10 replicate simulations with probabilities of pollen flow between adjacent arrays of 0.1 and 0.9, respectively. In both cases overall coexistence was obtained in the sense that at least one array always reached fixation for each of the two plant species. With increased pollen flow between arrays there was increased variance in the number of populations going to fixation for one or the other species. Once adjacent arrays have become fixed for different species, however, pollen flow is no longer a viable means for them to exchange colonists. For this reason, species compositions in the nine arrays remained constant once fixation was reached. An alternative to absolute restriction on seed exchange between arrays is to derive some fraction of the plants in each array at the onset of any generation from a seed pool representative of the overall fertilizations to species A and B in all arrays in the preceding generation. This was achieved with a subroutine which specifies a certain probability of making each seed choice from an overall seed pool. Seeds not chosen in this way were derived as before from seed pools within each individual array. Choosing seeds from the overall pool thus represents seed dispersal among all arrays. Figure 6 shows frequency distributions of the number of arrays out of nine which reached or approached within 20% of fixation of species A after 15 computer generations, from sets of 10 replicate simulations. In Figure 6A and B the probabilities of choosing seeds from the overall seed pool were 0.1 and 0.2, respectively; while that of pollinator flight between adjacent arrays

9 Interspecific Pollen Transfer and Competition 231 was 0.1. These small amounts of pollen and seed exchange did not lead to overall fixation for one species within 15 generations. However, increasing the probability of seed exchange from 0.1 to 0.2 clearly increased the tendency toward fixation. In Figure 6C and D the values of the seed flow term were again set at 0.1 and 0.2, while the pollen flow term was 0.9. With increased pollen flow between arrays the tendency toward rapid fixation for the same species in all nine arrays was greatly increased. Because seed exchange remains an effective means of colonizing arrays that have progressed to fixation for different species, the species compositions of individual arrays were still fluctuating at the end of 15 generations in cases where overall fixation had not occurred. Discussion Results from deterministic models of competition for pollination (Levin and Anderson, 1970; Waser, 1977) suggest that two co-occurring plant species subject to interspecific pollen transfer will not coexist indefinitely. Competitive exclusion also occurs in my simulations of pollination within a single mixed population of two species. Exclusion of one species occurs rapidly when pollinator visits, amounts of pollen flowing in the system, or stigma surfaces are chosen to be limiting relative to the total number of possible fertilizations in the population. Although pollination within a single array always leads to competitive exclusion in simulations, the duration of coexistence is extended when each species has a refugium which the competitor cannot colonize readily or at all. This underscores the fact that competition for space in addition to competition for pollination is implicit in the rules of simulations without refugia as well as in analogous deterministic models. Simulations with refugia represent situations in which co-occurring species share a pollinator but differ in edaphic requirements, and they should be extended in the future especially if such situations appear to be common in nature. It seems reasonable to expect that the probability of exclusion would be substantially reduced if the number of seed choices per refugial location were increased well beyond the values I have used. Coexistence in this case would require only that individual plants receive sufficient pollination on the average to replace themselves, rather than that both species receive equivalent pollination. The effect of refugia in my simulations was to limit seed but not pollen exchange between refugial columns in the array. Simulations with nine separate arrays represent a case in which both seed and pollen exchange are restricted between groups or populations of plants. With no seed exchange and little pollen exchange between populations overall coexistence of two species occurs because each goes to fixation in at least one population. Introducing seed exchange increases the likelihood of overall fixation for one competitor. However, small amounts of seed exchange may lead to fixation only after a very large number of generations if at all, so that coexistence is effectively achieved. The assumptions I have made concerning the effects of interspecific pollen transfer require some justification, since they differ in several respects from those of most other authors. (1) I assume that loss of pollen as a result of

10 232 N.M. Waser interspecific pollen transfer will commonly lead to reproductive effects. The absolute magnitudes of many pollen to ovule ratios (e.g., Ornduff, 1971, 1975b; Cruden, 1972, 1976, 1977) make pollen limitation appear unlikely at first, and some authors have explicitly asssumed unlimited pollen (e.g., Straw, 1972). However, it is becoming clear that only a small fraction of all pollen grains are involved in fertilization in real systems, due to infertility and loss during transport between flowers. For example, only about 4% of all pollen was both fertile and successfully deposited on a stigma in experiments with pollination of Phlox glabberima by butterflies (Levin, 1968b; Levin, and Berube, 1972). In addition, for several species there is now evidence that a pollen surplus on the order of 5-10 grains per ovule must reach the stigma for maximum fertilization to occur (Cruden, 1977). Effective pollen to ovule ratios may thus be up to three orders of magnitude lower than absolute ratios. These considerations imply that individuals exposed to interspecific pollen transfer will often suffer a reproductive loss either because pollen production cannot be increased or because doing so reduces allocation of resources to other functions affecting fitness. (2) I assume that loss of stigma surfaces to foreign grains may lead to competition, especially when a surplus of conspecific pollen relative to ovules is required for full seed set. For example, Delphinium nelsoni and Ipomopsis aggregata are herbaceous perennials which compete for hummingbird pollination, apparently by mechanisms involving interspecific pollen transfer, and each has receptive stigma surface sufficient to accept only 5-10 conspecific grains per ovule (Waser, 1977, 1978). If these surpluses are essential for full fertilization, seeds sets of the two species would be reduced by deposition of foreign grains. In discussing the evolution of heterostyly, Yeo (1975) also proposes that wastage of limited stigma surfaces could occur as a result of incompatible pollinations. Evidence suggestive of competition for limited stigma surfaces comes from Lithospermum caroliniense, in which mean percent seed sets of pin and thrum flowers vary inversely with stigmatic loads of incompatible pollen and do not reflect loads of compatible pollen (Levin, 1968a). (3) I assume that the partial or complete loss of effective pollinator visits implies that pollinators can be limiting even if the ratio of pollinators to flowers in a mixed population is no lower than that required for full fertilization in a population containing a single species. The rules of my simulations contain several important assumptions about the mechanics of pollination as well. (1) Pollinators visit flowers at random in a mixed population. This approximates the behavior of pollinator types which often exhibit incomplete or no flower constancy, such as hummingbirds (e.g., Grant and Grant, 1968; Waser, 1978), lepidopterans (e.g., Levin, 1968b; Levin and Berube, 1972; Kislev et al., 1972), and bumblebees and some solitary bees (e.g., Clements and Long, 1923; Brittain and Newton, 1933; Grant, 1950; Free, 1966, 1970a; Macior, 1970). (2) Pollen picked up at successive flowers is added to a pool on the pollinator's body from which grains are drawn at random and without replacement for deposit on stigmas. This allows pollen carryover past the first recipient flower, in contrast to deterministic models which lack carryover (Levin and Anderson, 1970; Waser, 1977). Extensive carryover and the random selection of pollen from a common pool on the pollinator's

11 Interspecific Pollen Transfer and Competition 233 body may be especially reasonable representations of flowers with highly exserted sexual parts (cf. Perkins, 1977). (3)The number of pollen grains picked up on each successive visit to any flower is constant rather than being a fixed proportion of the pollen remaining in the anthers of the flower. As I have found no data on this process in nature, I chose between alternative sets of rules on the basis of simplicity. (4) Finally, a pollinator has equal probabilities of moving in each of four directions after leaving any flower. This is an oversimplification since directionality in pollinator foraging movements has been documented (Pyke, 1974). I do not expect lack of directionality to have changed the qualitiative outcome of simulations, however, since the sequence of flowers encountered in a randomly mixed population is close to random regardless of directionality. The absolute values chosen for the number of pollen grains involved in the pollination cycle were unrealistically small in simulations and may have led to sampling error effects in some cases. However, I chose biologically reasonable ratios for amounts of pollen involved in different phases of pollination (see Table 1). For example, the ratio of the initial pollen in anthers to the number of grains picked up in each pollinator visit was 10:1 in most simulations. This agrees with the ratio reported by Levin and Berube (1972) for butterflies visiting two species of Phlox. The 10:3 ratio of pollen grains picked up to those deposited in each visit is also reasonable (Levin and Berube, 1972). Most simulations used a 20:1 ratio of initial pollen in anthers to stigma capacity, which agrees with some natural systems (Levin and Berube, 1972; Ornduff, 1975a; Cruden, 1976, 1977) but underestimates ratios in others (Ornduff, 197l, 1975b; Cruden, 19'72, 1976, 1977). Simulations do not allow for pollen loss between production and fertilization, however. Even the 3 : 5 ratio used in simulations investigating pollen limitation falls within the range of values reported for natural systems when the latter are corrected for pollen loss. Finally, the pollen capacity of stigmas exceeded the number of grains deposited in a single pollinator visit so that multiple visits were necessary for full pollination. This is surely the case for many plant species (e.g., Cruden et al., 1976). To this point I have emphasized animal pollinators in discussing competition for pollination, and my simulations are direct attempts to model competition in a system with animal-mediated pollen flow. However, competition might also occur in some wind pollinated systems. The necessary condition in such cases is for interspecific pollen transfer to cause some loss of pollen or stigma surfaces which would otherwise contribute to fertilization events. The loss of stigma surfaces seems likely to be the more important mechanism for wind pollinated plants. Overall coexistence of two competitors was obtained only in simulations of a series of populations separated by strong barriers to seed and pollen flow. This suggests first of all that spatial subdivision of a meadow into partly isolated patches will facilitate coexistence of potential competitors in real biological systems. Coexistence will occur as long as each plant species goes to fixation in some habitat patches. In nature the physical distances necessary to prevent seed and pollen flow between patches might be on the order of only meters or tens of meters, especially given the short distances over which the majority

12 234 N.M. Waser of pollen grains and seeds are dispersed in many systems (Levin and Kerster, 1974). Pollinators which defend or return to distinct foraging areas that remain fairly stable during the receptive period of single flowers or plants might also play an important role in subdividing initially homogeneous mixtures of competitors, even if the exact locations of foraging areas change from year to year. Temperate hummingbirds often defend small feeding territories on the order of 0.1 ha or less for periods of several days at least (Armitage, 1955; Grant and Grant, 1968; Stiles, 1973; Lyon, 1973). Bumblebees may also work small patches of meadow covering a few square meters over periods of several days (Grant, 1950; Free, 1966, 1970b). Although they do not address directly the dynamics of temporal divergence, simulations with separate populations suggest that overall coexistence could also occur when two potential competitors for pollination differ sufficiently in flowering time. Further simulations with refugia may identify situations in which rapid competitive exclusion would be avoided in homogeneous mixtures of simultaneously flowering species which differ in edaphic requirements. Even so, I expect that differences in flowering time will evolve in many such systems in nature, because sequential flowering will reduce the reproductive losses caused by interspecific pollen transfer. Thus, individual plants which flower during a period devoid of flowering competitors should displace conspecifics whose flowering overlaps that of competitors unless counterbalancing forces act to restrict flowering time. The simulations with separate populations can be taken to depict a flowering season divided into time slots which overlap slightly or not at all, each of which is occupied by one of several species sharing a pollinator. Alternatively they might depict the division of each day into separate periods during which each of several competitors is receptive and produces floral rewards for pollinators (cf. Synge, 1947; Percival, 1955; Gilbert, 1975; Parrish and Bazzaz, 1976). The evolution of temporal divergence requires only some original heritable variation in individual flowering overlap with competitors upon which selection can act. The degree to which complete divergence is achieved or maintained in nature should depend on how accurately proximate cues available for the timing of flowering predict the flowering state of competitors, and on other selective forces influencing flowering time such as density-dependent visitation by pollinators or attack by predators (cf. Holling, 1959; Augspurger, 1977), overall lengths of appropriate seasons for flowering or vegetative growth, or optimal timing for seed maturation and dispersal and seedling establishment. In summary, simulations of a pollinator foraging at random within a single mixed population confirm the expectation that interspecifc pollen transfer can lead to competitive interactions if pollen, stigma surfaces, or pollinator movements are limiting to reproduction. In addition, simulations of pollination in a series of partially isolated populations provide insight into potential evolutionary changes which would reduce competition for pollination. In these simulations reproductive losses to individual plants are reduced by decreasing pollinator sharing and pollen flow between flowers of two competitors. Because differences in habitat affinity or flowering time can prevent interspecific pollen transfer, I conclude that such differences will commonly appear among co-occurring species which share pollinators.

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